On the stabilizing conic sectors obtained using small-gain techniques

Abstract This paper is concerned with the analysis of the scope and properties of the stabilizing conic sectors obtained using small-gain and loop-transformation (SGLT) techniques. First, it is shown how SGLT techniques are able to generate the set of all nonlinear stabilizing controllers by using transformations based on dynamical 2 × 2 block systems (configurations). Then, stabilizing cones obtained from static configurations are considered. They induce only subsets of all stabilizing controllers, however, providing simplification and tractability. For these cones, maximality is characterized in terms of mu values and frequency responses, finally, an algorithm for deriving maximal cones is presented.

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